Charge fluctuations in open chaotic cavities

Abstract

We present a discussion of the charge response and the charge fluctuations of mesoscopic chaotic cavities in terms of a generalized Wigner-Smith matrix. The Wigner-Smith matrix is well known in investigations of time-delay of quantum scattering. It is expressed in terms of the scattering matrix and its derivatives with energy. We consider a similar matrix but instead of an energy derivative we investigate the derivative with regard to the electric potential. The resulting matrix is then the operator of charge. If this charge operator is combined with a self-consistent treatment of Coulomb interaction, the charge operator determines the capacitance of the system, the non-dissipative ac-linear response, the RC-time with a novel charge relaxation resistance, and in the presence of transport a resistance that governs the displacement currents induced into a nearby conductor. In particular these capacitances and resistances determine the relaxation rate and dephasing rate of a nearby qubit (a double quantum dot). We discuss the role of screening of mesoscopic chaotic detectors. Coulomb interaction effects in quantum pumping and in photon assisted electron-hole shot noise are treated similarly. For the latter we present novel results for chaotic cavities with non-ideal leads.